SYNOPSIS

SUBROUTINE SPPTRF(

UPLO, N, AP, INFO )

    

CHARACTER UPLO

    

INTEGER INFO, N

    

REAL AP( * )

PURPOSE

SPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. The factorization has the form

   A = U**T * U,  if UPLO = 'U', or

   A = L  * L**T,  if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.

ARGUMENTS

UPLO (input) CHARACTER*1

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N (input) INTEGER

The order of the matrix A. N >= 0.

AP (input/output) REAL array, dimension (N*(N+1)/2)

On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

FURTHER DETAILS

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':
Two-dimensional storage of the symmetric matrix A:

   a11 a12 a13 a14

       a22 a23 a24

           a33 a34     (aij = aji)

               a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]